Question: Rectangle $ABCD$ is the base of pyramid $PABCD$. If $AB = 8$, $BC = 4$, $\overline{PA}\perp \overline{AD}$, $\overline{PA}\perp \overline{AB}$, and $PB = 17$, then what is the volume of $PABCD$?
Answer: [asy]
import three;
triple A = (4,8,0);
triple B= (4,0,0);
triple C = (0,0,0);
triple D = (0,8,0);
triple P = (4,8,6);
draw(B--P--D--A--B);
draw(A--P);
draw(C--P, dashed);
draw(B--C--D,dashed);
label("$A$",A,S);
label("$B$",B,W);
label("$C$",C,S);
label("$D$",D,E);
label("$P$",P,N);
[/asy]

Since $\overline{PA}$ is perpendicular to both $\overline{AB}$ and $\overline{AD}$, the segment $\overline{PA}$ is the altitude from the apex to the base of the pyramid.   To find this length, consider right triangle $PAB$.  Applying the Pythagorean Theorem gives $PA = \sqrt{PB^2 - AB^2} = 15$.

The area of the base is $[ABCD] = (AB)(BC) = 32$, so the volume of the pyramid is $\frac13(32)(15) = \boxed{160}$ cubic units.